Can anyone explain the role of Tools > Programmer and why/ when we should select one of the various options given such as: AVR ISP, AVR ISP mkii, USB asp etc. And say if i were using the Virtual COM port 6 to burn a sketch into the arduino board, which one of the options should be set by me?

IF you have a programmer, you use one of those options. If you're simply uploading via a USB cable, you don't need to worry about it. However, if you've purchased an external programmer, such as the AVR-ISP, an stk500, or even if you're uploading via an ArduinoISP, you'll be selecting one of those options and instead of hitting Upload, you'd hit Upload Using Programmer (look under the File menu).

The selection is ignored if you are not using an AVR ISP Programmer to burn a bootloader or a sketch via the ICSP header.

The message you see when downloading via the serial port (USB) indicates the chip is not responding.Try a different cable, try the Loopback Test (see programming forum), confirm the chip has a bootloader installed.